The clinical applications of testosterone in women are predicated upon the postulate that by appropriate selection of testosterone dose, clinically beneficial effects of testosterone on sexual, physical and neurocognitive functions can be dissociated from its virilizing side effects. However, we do not know whether the skin, hair, vocal cords, and clitoris differ in their testosterone sensitivity from sexual, cognitive, and physical functions. Therefore, the primary objective of this study is to establish testosterone dose-response relationships in surgically menopausal women with low testosterone concentrations for a range of androgen-dependent outcomes, including sexual function, fat-free mass, thigh muscle strength and leg power, and several domains of neurocognitive function. The secondary objective is to determine the range of testosterone doses and concentrations that are associated with improvements in sexual, physical and neurocognitive functions and that can be safely administered to women without adverse effects on hair growth, voice, sebum production, clitoral size, and cardiovascular risk factors. In this randomized, double-blind, parallel-group study, surgically-menopausal women with low testosterone concentrations after a run-in period of transdermal estradiol for 3 months will be randomized to one of 4 groups to receive 0, 400, 1000, or 1600 uL testosterone gel daily for 6-months. These doses are expected to be associated with total testosterone concentrations of 20, 60, 120, and 180 ng/dL. The following outcomes will be assessed before and after 24-weeks of testosterone/placebo: sexual function, assessed by Brief Index of Sexual Functioning for Women, Derogatis Sexual Function Interview-Self Report, a sexual event log diary, and a Female Sexual Distress Scale; genital blood flow and sensation; mood by Psychological General Well Being Index; whole body and regional fat-free and fat mass by DEXA, deuterium water and sodium water dilution; and MRI scans of abdomen and thigh; leg press strength and leg power; physical function by Margaria power test, 400-m walk, and load carry test; and neurocognitive function by tests of spatial memory, spatial ability, logical memory, verbal (category and phonemic) fluency, immediate and delayed recall, digit and visual memory spans, spatial orientation, selective attention measure, and executive function. We will measure serum total and free testosterone, estradiol, DHT, SHBG, and FSH. For safety, we will evaluate hematocrit, liver enzymes, periodic breast and pelvic examination, hair growth by Ferriman and Galloway scale, sebuln production by Sebu-Tape, acne by Palatsi scale, clitoris size and index, changes in voice frequency, pitch range, and video images of vocal cords and digital speech records; plasma lipids, apolipoproteins and lipoprotein particles; inflammation sensitive markers; sleep apnea using Berlin's questionnaire; and insulin sensitivity by modified FSIVGT. These dose response data are crucial for the therapeutic applications of androgens in women, and will help determine whether by appropriate selection of testosterone dose, its beneficial effects can be dissociated from virilizing side effects.